The long range objectives of this research are to further our understanding of signal transduction and gene control networks, particularly as they relate to pattern formation in developmental biology. The work involves analysis of specific biological systems, as well as the development of general analytical and computational techniques. The (major projects are: (1) studies on pattern formation in Drosophila and limb development, and (2) studies on signal transduction, motor control and pattern formation in E. coli. The aim under (1) are the development, analysis and testing of models of patterning along the dorsal-ventral axes in early embryonic development of Drosophila, and of patterning and the effects of growth and shape changes in the wing discs in Drosophila The aims under (2) are to understand the origin of high gain in signal transduction in E. coli by analyzing models of receptor clustering, to incorporate new receptor models into a complete model for the chemotactic signal transduction pathway, to integrate this model with a model for the control of the flagellar motor, and to understand macroscopic, population-level spatial patterns using detailed models of individual behavior. In both of these projects a significant task will be to understand how the topology of signal transduction and gene control networks affects the stochastic fluctuations of components in the network, and thereby to understand what patterns of interactions ensure reliable outputs. The research in (1) will advance our understanding of basic processes in developmental biology such as signal transduction, gene control, and pattern formation. A better understanding of these fundamental processes will contribute to a better understanding of how systems respond to their environment, how normal development can be disrupted and perhaps how abnormal development can be corrected. The results of the work in (2) will contribute to our understanding of how extracellular signals are transduced into motor control in bacteria, how the microscopic behavior of individuals is reflected in population-level descriptions, and how nutrient supply and chemotactic factors control pattern formation. This result will provide insight into factors that are involved in the formation of biofilms. [unreadable] [unreadable] [unreadable]